Asha Gopalakrishnan; Dr.Unnikrishnan Nair, N(Cochin University Of Science And Technology, May 15, 1995)
[+]
[-]
Abstract:
The term reliability of an equipment or device is
often meant to indicate the probability that it carries out
the functions expected of it adequately or without failure
and within specified performance limits at a given age for a
desired mission time when put to use under the designated
application and operating environmental stress. A broad
classification of the approaches employed in relation to
reliability studies can be made as probabilistic and
deterministic, where the main interest in the former is to
device tools and methods to identify the random mechanism
governing the failure process through a proper statistical
frame work, while the latter addresses the question of
finding the causes of failure and steps to reduce individual
failures thereby enhancing reliability. In the
probabilistic attitude to which the present study subscribes to, the concept of life distribution, a mathematical
idealisation that describes the failure times, is
fundamental and a basic question a reliability analyst has
to settle is the form of the life distribution. It is for
no other reason that a major share of the literature on the
mathematical theory of reliability is focussed on methods of
arriving at reasonable models of failure times and in
showing the failure patterns that induce such models. The
application of the methodology of life time distributions is
not confined to the assesment of endurance of equipments and
systems only, but ranges over a wide variety of scientific
investigations where the word life time may not refer to the
length of life in the literal sense, but can be concieved in
its most general form as a non-negative random variable.
Thus the tools developed in connection with modelling life
time data have found applications in other areas of research
such as actuarial science, engineering, biomedical sciences,
economics, extreme value theory etc.
Description:
Division of Statistics, School of Mathematical Sciences,
Cochin University of Science and Technology
Muraleedharan Nair,K R; Dr.Unnikrishnan Nair, N(Cochin University Of Science And Technology, May 10, 1990)
[+]
[-]
Abstract:
It is highly desirable that any multivariate
distribution possessescharacteristic properties that
are generalisation in some sense of the corresponding
results in the univariate case. Therefore it is of
interest to examine whether a multivariate distribution
can admit such characterizations. In the exponential
context, the question to be answered is, in what meaning—
ful way can one extend the unique properties in the
univariate case in a bivariate set up? Since the lack
of memory property is the best studied and most useful
property of the exponential law, our first endeavour
in the present thesis, is to suitably extend this
property and its equivalent forms so as to characterize
the Gumbel's bivariate exponential distribution.
Though there are many forms of bivariate exponential
distributions, a matching interest has not been shown
in developing corresponding discrete versions in the
form of bivariate geometric distributions. Accordingly,
attempt is also made to introduce the geometric version
of the Gumbel distribution and examine several of its
characteristic properties. A major area where exponential
models are successfully applied being reliability
theory, we also look into the role of these bivariate
laws in that context.
The present thesis is organised into five
Chapters
Description:
Department of Mathematics
and Statistics, Cochin University of Science
and Technology
This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.
Description:
Department of Statistics, Cochin
University of Science and Technology
Thomas, Joseph; Dr.Jathavedan, M(Cochin University of Science and Technology, June , 1993)
[+]
[-]
Abstract:
This thesis contains a study of conservation laws of
fluid mechanics. These conservation laws though classical, have
been put to extensive studies in t:he past many decades
Description:
Department of Mathematics And Statistics, Cochin University of Science And Technology
Sreekumar, R; Thrivikraman,T; Chakravarti, R S(Department of Mathematics, Faculty of Science, 2002)
[+]
[-]
Abstract:
The main purpose of the study is to extent concept of the class of spaces called ‘generalized metric spaces’ to fuzzy context and investigates its properties. Any class of spaces defined by a property possessed by all metric spaces could technically be called as a class of ‘generalized metric spaces’. But the term is meant for classes, which are ‘close’ to metrizable spaces in some under certain kinds of mappings. The theory of generalized metric spaces is closely related to ‘metrization theory’. The class of spaces likes Morita’s M- spaces, Borges’s w-spaces, Arhangelskii’s p-spaces, Okuyama’s spaces have major roles in the theory of generalized metric spaces. The thesis introduces fuzzy metrizable spaces, fuzzy submetrizable spaces and proves some characterizations of fuzzy submetrizable spaces, and also the fuzzy generalized metric spaces like fuzzy w-spaces, fuzzy Moore spaces, fuzzy M-spaces, fuzzy k-spaces, fuzzy -spaces study of their properties, prove some equivalent conditions for fuzzy p-spaces. The concept of a network is one of the most useful tools in the theory of generalized metric spaces. The -spaces is a class of generalized metric spaces having a network.
Babu, Sundar S; Dr.Thrivikraman, T(Cochin University Of Science And Technology, March 21, 1989)
[+]
[-]
Abstract:
It is believed that every fuzzy generalization should be
formulated in such a way that it contain the ordinary set
theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9]
with an arbitrary complete and distributive lattice as the
membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy
topologies on a set. It is proved that in general, the
lattice of fuzzy topologies is not complemented. Complements
of some fuzzy topologies are found out. It is observed that
(L,X) is not uniquely complemented. However, a complete
analysis of the problem of complementation in the lattice
of fuzzy topologies is yet to be found out
Description:
Depantment of Mathematics and Statistics
Cochin University of Scince
and Technology
Baby,B V; Dr.Babu, Joseph K(Cochin University of Science and Technology, April 3, 1985)
[+]
[-]
Abstract:
An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes
one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear
operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.
Description:
Department of Physics, Cochin University of Science and Technology
Rosa, M V; Dr.Thrivikraman, T(Cochin University Of Science And Technology, May 6, 1994)
[+]
[-]
Abstract:
This thesis is a study of abstract fuzzy convexity
spaces and fuzzy topology fuzzy convexity spaces No attempt seems to have been made to develop
a fuzzy convexity theoryin abstract situations. The
purpose of this thesis is to introduce fuzzy convexity
theory in abstract situations
Description:
Department
of Mathematics and Statistics, Cochin University of
Science and Technology
Ramachandran,P T; Dr.Thrivikraman, T(Cochin University of Science and Technology, 1985)
[+]
[-]
Abstract:
In this thesis we investigate some problems in set theoretical topology related to the concepts of
the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms.
This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention
Description:
Department of Mathematics and Statistics, Cochin University of Science and Technology
Velukutty, K K; Dr.Wazir, Hasan Abdi(Cochin University of Science and Technology, February 15, 1982)
[+]
[-]
Abstract:
An attempt is made by the researcher to establish a theory of discrete functions in the complex plane. Classical analysis q-basic theory, monodiffric theory, preholomorphic theory and q-analytic theory have been utilised to develop concepts like differentiation, integration and special functions.
Description:
Department of Mathematics and Statistics, Cochin University of Science & Technology